Q.332. - Intermediate Algebra

Question

Use the remainder theorem to find the remainder.

$f\left(x\right)=2x^3-6x-24$ divided by $x-3$.

Step-by-Step Solution

Answer

The solution is $12$.

Step 1. Given information.

$f\left(x\right)=2x^3-6x-24$ is divided by $x-3$.

Step 2. To find the remainder.

Write the divisor $x-3$ in the form $x-c$, so $c$ is $3$.

Substitute $x=3$ in $f\left(x\right)=2x^3-6x-24$.

$$\begin{gathered} f\left(3\right)=2{\left(3\right)}^3-6\left(3\right)-24 \\ \Rightarrow 54-18-24 \\ \Rightarrow 12 \end{gathered}$$

Step 3. Simplified answer.

Hence, the remainder is $12$.